b * charged a miji , beI ° W ' Yo ° "«/
JAN 4 2000
PAPER NO. 89-1526
Moral Hazard, Limited Entry
Costs, and "Introductory Offers"
THE LIBRAKY OY THE
a 2 1989
Hadi S. Esfahani
WORKING PAPER SERIES ON THE POLITICAL ECONOMY OF INSTITUTIONS
College of Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois Urbana-Champaign
Digitized by the Internet Archive
in 2011 with funding from
University of Illinois Urbana-Champaign
FACULTY WORKING PAPER NO. 89-1526
College of Commerce and Business Administration
University of Illinois at Urbana- Champaign
Moral Hazard, Limited Entry Costs, and 'Introductory Offers'
Hadi S. Esfahani, Assistant Professor
Department of Economics
I have benefitted from helpful comments of Lanny Arvan, Charles Kahn,
and Pablo Spiller on earlier drafts of this paper.
This paper develops a game-theoretic model of a market for a high
quality product that is subject to moral hazard. It uses "introductory
offers" to reconcile free entry with existence of premia necessary for the
maintenance of high quality. Buyers boycott sellers who cheat and continue
purchasing from established sellers whose offers are not dominated by those
of entrants. In equilibrium, entrants charge a lower price than established
sellers and provide the high quality with a smaller frequency. The entry
price is sufficiently low to render the expected profits from entry equal to
zero, despite high quality premia. The model avoids the restrictive assump-
tions of previous models such as irrational expectations on the part of
buyers and time inconsistency on the part of sellers.
This paper develops a game-theoretic model of a market for a high
quality product that is subject to moral hazard. It uses "introductory
offers" to reconcile free entry with the existence of premia necessary for
the maintenance of high quality while avoiding the restrictive assumptions
of previous models.
In markets where product quality is observable only after purchase,
sellers have an incentive to sell "lemons" in place of more costly high
quality products (Akerlof, 1970). However, if purchases can be repeated,
there is a potential for this seller moral hazard to be overcome through
buyers' use of a trigger strategy. If buyers boycott sellers who cheat,
then sellers will have an incentive to produce high quality products as long
as they expect to earn sufficiently high rents from their continued opera-
tion in the market. In the presence of large exogenous entry costs,
expected future profits from reputation maintenance may be large enough to
outweigh the short-run benefits of cheating and, thus, to make high quality
production a profitable strategy.
When exogenous nonsalvageable entry costs are small, sustainable profits
may be too low to induce high quality production. In this situation, high
quality products will be sold only if other mechanisms exist to maintain the
necessary incentives. Third party verification is one such mechanism.
However, given the difficulties for a third party to verify the claims of
sellers and buyers concerning quality, which often consists of a number of
hard-to-measure product characteristics, the existence of the market for
high quality products ultimately hinges upon "endogenous" mechanisms.
Several examples of such mechanisms have been modeled in the literature on
reputation and product quality (Klein and Leffler, 1981; Shapiro, 1983;
Allen, 1984; Farrell, 1986).
In a seminal paper, Klein and Leffler (1981) argued that when exogenous
entry costs are too low to sustain the premia necessary for high quality
maintenance, sellers will precoramit themselves to the provision of "free"
services that are valuable to buyers. This precoramitraent is achieved by
sellers investing in nonsalvageable assets that render those services.
However, as Allen (1984) points out, for most industries such services are
either not feasible or have the nature of public goods and, therefore, are
unlikely to attract buyers to the firm providing them.
Allen (1984), in turn, develops a model in which there are no endogenous
entry costs and the problem of excessive entry in the high quality market is
solved by sellers operating at scales that are suboptimally small for the
price they charge. Sellers do not cut their prices because it makes cheating
more profitable, and buyers — who are aware of this relationship — would not
buy their products. In equilibrium, established sellers earn sufficient
premia over their recurrent average costs to have the necessary incentives
to provide the high quality. The equilibrium number of firms in the market
is such that the sales of each firm are just sufficient to provide entrants
with zero discounted long-term profits, given some exogenous entry costs.
The exogenous entry costs must be positive, but not necessarily large, for
the equilibrium output of each firm to be greater than zero.
An implicit assumption crucial for the existence of an equilibrium in
Allen's model is that sellers must be able to precommit themselves to a
price in all future periods. In the absence of such an assumption, a seller
can claim that he is reducing his price and expanding his output only for
one period and will go back to the "equilibrium" path thereafter. If buyers
believe that such an equilibrium exists, it becomes possible to deviate in
this way without violating the seller moral hazard condition, since it is
only the future profits that provide sellers with the necessary incentive to
maintain their reputations. Therefore, the deviating strategy has the poten-
tial to make the seller as well as his customers better off. Obviously,
this possibility encourages deviation from the equilibrium path in each
period by every seller, which ultimately upsets the equilibrium.
Shapiro (1983) analyzes an alternative mechanism for generating endoge-
nous entry costs. He builds an "adaptive expectations" model in which in
any given period buyers expect each seller to supply a quality similar to
what he has marketed in the past. In the case of entrants, buyers expect
the worst quality. This forces entrants to offer low introductory prices
while they provide high quality products. Shapiro shows that the endogenous
entry costs generated in this way may be sufficient to support a high
quality equilibrium. However, if buyers are rational, the equilibrium
collapses since in this case buyers would prefer to purchase from entrants
and not from established sellers.
Farrell (1986) argues that moral hazard itself may serve as an entry
barrier if entrants are expected to have low profits in the future. This
may happen if firms are large and entry by each single firm has a non-
negligible impact on the market. In this case, entry with the promise of
high product quality may not be credible if buyers do not find switching
sellers worthwhile or anticipate effective reactions by incumbents.
In the model developed in this paper, buyers' expectations are assumed
to be rational and the existence of equilibrium does not depend on exogenous
entry costs, large firm sizes, or sellers' ability to commit themselves to
free services or fixed prices. The main assumption of the model that gives
rise to a mechanism for endogenous entry costs is that each buyer continues
to purchase from the same seller as long as the seller does not cheat or
make offers that the buyer finds inferior to those he expects from other
sellers. This type of buyer behavior puts entrants at a slightly disadvan-
taged position vis-a-vis incumbents and forces them to offer a lower price
and incur an "entry" cost. Competition among entrants then reduces the
entry price to a level just sufficient to sustain the premiums necessary for
quality maintenance. Despite this price difference, entrants and incumbents
have the same incentives to produce the high quality since the quality deci-
sion by sellers depends only on future profits. In equilibrium, all sellers
are indifferent between providing the high quality and cheating and, thus,
randomize their quality decision. Even though the price offered by entrants
is lower than that of incumbents, buyers remain indifferent between the two
groups and continue purchasing from incumbents because entrants provide the
high quality with a smaller frequency. This happens because any increase in
the expected probability of high quality provision by entrants makes their
offers more attractive to buyers and forces incumbents to lower their pri-
ces, which in turn diminishes the value of becoming established and induces
entrants to cheat more often.
II. The Model
Consider a product that can be produced with two different qualities; a
high quality (H) and a low quality (L) . Suppose that each seller produces
one unit of the product in each period, with the cost depending on quality.
Let c be the unit cost of producing quality q, q = H,L, where c^ > c > 0.
Assume that in each period, each buyer purchases one unit of the product and
deals with only one seller. Let u be the buyers' monetary valuation of
quality q, q ■ H,L. To simplify the analysis, we assume that u, = and
it, > Crr so that only the high quality is worth producing. All buyers and
sellers are infinitely-lived and risk neutral. For sellers who leave the
market or those who remain outside, the per-period expected profits are nor-
malized to zero. Similarly, the utility of buyers who do not purchase the
product is assumed to be equal to zero.
At the beginning of each period, first each buyer decides whether to
consider the offer of the seller from whom he has purchased in the previous
period or to seek another seller. We will call a seller who has a con-
tinuing customer an established seller. All other sellers are considered
entrants. Each established seller first announces the price and the quality
of his product to his current customer. If the buyer accepts the offer,
trade takes place, otherwise the buyer costlessly searches out offers from
among the pool of entrants. In the latter case, the established seller
becomes an entrant. After the fate of the offers by established sellers is
determined, all entrants announce their price-cum-quality offers. We model
the buyer search behavior among entrants by assuming that buyers are ran-
domly matched among entrants so that if there is any unmatched seller, then
his offer provides buyers with an expected consumer surplus that does not
exceed the expected consumer surplus implied by the offers of the matched
sellers. After this matching, there is another stage where offers are
accepted or rejected. Finally, buyers experience the actual qualities of
the products they have received and, then, the play proceeds into the sub-
Because we wish to focus on the seller moral hazard, we posit the
following in regard to buyer strategies. First, at the beginning of a
period, a buyer decides not to consider the offer of the seller from whom he
has purchased in the previous period if at any time in the past that seller
has cheated by announcing the high quality and delivering the low quality.
Second, when a buyer decides to consider the offer of an established seller,
he rejects it if the expected consumer surplus implied by the offer is less
than the expected consumer surplus that would result if the buyer sought the
offer of an entrant. Finally, when a buyer is matched with an entrant, the
buyer accepts the entrant's offer if the expected consumer surplus resulting
from the offer is nonnegative, otherwise the buyer does not trade at all in
that period. Given the behavior of sellers modeled below, it is not hard to
show that this buyer behavior is consistent with perfect equilibrium.
Since the low quality product has no value for buyers, when a seller
announces the low quality, he is better off not producing the product at
all. Thus, it seems reasonable to assume that an offer which includes the
low quality simply involves a payment (a nonpositive price) from the seller
to a buyer who promises to consider the seller's offer at the beginning of
the following period. A close examination of the model should make it clear
that changing this assumption to a case where the low quality product has to
be produced and delivered in order for buyers to stay with their current
sellers who offer the low quality does not change the basic results of the
The goal of the following analysis is to show that if the high quality
is sufficiently valued by buyers such that
^) U H > C H + Cl+r)(c H -c L ),
then the model described above has a subgame perfect equilibrium where the
entry is free and established sellers always produce the high quality.
As we will show below, condition (1) simply states that the utility of buy-
ing the high quality from an established seller should exceed the cost of
production by at least r(c -c ), which is the minimum premium necessary to
overcome the seller moral hazard, plus C..-C. , which is the maximum bonus
that in equilibrium entrants are willing to offer to lure away customers
from established sellers.
To analyze the equilibria of the model, let us begin by considering an
established seller who offers quality q at price p to his customer in period
t. Let V be the discounted present value of the seller's expected profits
from period t+1 onwards if he remains established in that period. Since we
are going to assume free entry, the value of being an entrant in period t+1
can be set equal to zero. Note that an established seller can always choose
to become an entrant. Therefore, we will have V >_ 0. Suppose the buyer
accepts the offer (p,q). Let a be the probability that the seller chooses
the high quality. If q = L, the seller will not supply the high quality
product since it will cost him c^ in the current period without providing
any further benefit in future. Therefore, in this case a ■ 0. However, if
q = H, the seller will supply the high quality only when the benefits of
remaining established do not fall short of the gains from cheating; that is,
^ V ^ C H-V
where r is the rate of interest. If (2) holds with a strict inequality, the
seller can do best by setting a = 1, while if (2) holds with an equality, a
can be anywhere between and 1. In light of these observations, it is
reasonable to assume that after observing the offer (p,q), the buyer will
expect the high quality to be supplied with probability B defined by
(3) 3=1 if q = H and -^ V > c R - c^;
< 3 < 1 if q = H and -r— v = c u - c. ; and
— — L + r H L
Note that the current price, p, does not play any role in the buyer's
belief formation since once the price is paid, it is sunk and does not enter
the seller's quality decision. However, p does play a role in the buyer's
decision whether to accept the offer or not. Suppose that the buyer expects
net utility u„ >. if he goes to an entrant. Then he accepts (p,q) only if
(4) p < gujj - u Q .
It should be noted that since an established seller has a first-mover
advantage, the buyer cannot expect any rents from being attached to the
seller and, therefore, any price higher than 0u^ - u n is not worthwhile for
him to accept.
Among acceptable offers, given q, the seller can do best by choosing p
such that (4) holds with an equality. When q = H, the long-terra profits of
the seller can be written as tt„ = p - etc - (l-a)c + aV/(l+r). The maximum
rl ti L
value of these profits is
(5) irj - Su H - u Q - c L + «[JL- (c H -c L )].
In this case, the seller will be interested in making an acceptable offer
only if tt* > 0, otherwise he will be better off becoming an entrant.
Therefore, when q = H, the seller will choose p such that
(6) p = Bu^ - u Q if tt* > 0; and
P > BUg - u Q if tt* < 0.
When q = L, the expected profits are tt = p + V/(l+r) with the maximum
value of it* = -u n + V/(l+r). In this case, the price will be chosen accord-
(7) p = -u Q if tt*_> 0; and
p > -u if it* < 0.
Note that as pointed out above, when q = L, acceptable prices are nonposi-
The optimal choice of q depends on the relative values of tt* and tt*.
When tt* and tt* are both negative, the choice of q does not matter in equi-
librium, because the seller will not make acceptable offers anyway. However,
by taking into account the possibility of an out-of-equilibrium move by the
buyer to accept an offer that violates (4) we can restrict the choice of q
in this case to L since for any given price, p, we always have tt < tt .
Therefore, we have
(8) q = H if tt* > tt* and tt* > 0; and
n — L rl —
q = L otherwise,
It is assumed that when rr* = tt* > , the seller chooses q = H.
rl L —
We now need to specify what happens if the buyer goes to an entrant.
Suppose that the buyer is considering an offer (p ,q ) from an entrant.
Since an entrant who finds a customer has exactly the same incentives as
those of an established seller, the quality decision of the entrant, y> and
the belief of the buyer regarding the probability of high quality provision
by the entrant, u, can be summarized by
(9) y = U = 1 if q £ = H and — V > c H - c L ;
< y and u < 1 if q = H and — — V = c - c ; and
— — h l + r H L
Y = U = otherwise.
The buyer accepts the offer (p ,q ) from the entrant only if yu^ - p >_
0, otherwise he is better off not buying at all, in which case u n = 0.
Therefore, u~ is given by
(10) u Q = MUjj - p E if uiijj - p E > 0; and
U = ° if UU H " P E < °-
Under a free entry condition, entrants should not be able to make posi-
tive profits. This implies that when q F = L, p„ + V/(l+r) _< 0. Since in
this case acceptable offers must satisfy p < 0, the optimal choice of p
from the entrant's point of view is
(id p E --Tf? v -
When q = H, we must have p - c„ + V/(l+r) < and p - c < 0. Given the
b EH — L L —
acceptability condition p <_ uu„ , the choice of p associated with q„ = H
can be described by
< 12 > p e " c l " * [ T?F v - ( V c l )] lf uu h ^ c l ' Y[ TJF v - ( V c l >,; and
p £ > c L - YtTTI v ~^ c h " c t )1 otherwise.
The entry strategy that dominates should yield the highest consumer
surplus for buyers. Therefore, taking into consideration the implications
of the out-of-equilibrium moves as in the case of established sellers, we
(13) q E = Hif %^ V + c L' Yti-V-CvVl; and
q^ = L otherwise.
Given V, a one-period rational expectations equilibrium of the model is
defined by a set of values for p, q, a, 3, p„ , q_ , Y» U > and u n that satisfy
E E U
a = 3, y ■ M, (3), and (6)-(13). It is easy to see that for V > (l+r)(c -c^),
the equilibrium conditions yield a=3=Y = U = l> q = q„ = H, p = p = c
- V/(l+r), and u = u + V/(l+r) - c u > 0. For V < (l+r)(c -c T ) , an equi-
U n H H L
librium exists ata=3=Y = U = 0> q = q=L, p = p - V/(l+r), and u n =
V/(l+r). Finally, for V = (l+rKc^-c. ) , two sets of equilibria exist. In
the first set of equilibria, y = M = 0, q„ = L, p„ = c T - c„ , and u n = c -
E E L rl U rl
c^ . In this case, either a = 3 _> c /u.., q = H, and p = 3u„ ~ ^ c u -c r ) » or
a=3 = 0, q = L, and p = c. - c„. In the second set of equilibria, y = \i >_
c /u^, q = H, p = c , and u = \iu - e. In this case, if a = 3 _> U,
established sellers trade at q = H and p ■ (3 - u)u„ + c , and if \i =
c^/u^ and a = 3 = 0, they trade at q = L and p = c^ - c , otherwise they set
q = L and make unacceptable offers.
The stationary equilibria of the model can now be characterized by
determining V. Obviously, in a stationary equilibrium we must have either
V = tt* or V = it* depending on the value of q. Note that the model does not
have a stationary equilibrium where all sellers provide the low quality
since buyers are not interested in purchasing the low quality at any positive
price. Therefore, if the market is active at all, 8 or p must be positive.
In particular, 3 must be positive since 3 = implies either V = tr* < or
V = tt* < 0, which are both inconsistent with an equilibrium that involves
trade. From 6 > and condition (3) it immediately follows that in equil-
ibrium we must have q = H and V _> (l+r)(c -c ). However, V > (l+r)(c -c,)
can be ruled out since in that case, V > = tt* > tt*. Thus, in a stationary
equilibrium, V = (l+r)(c -c ). Since V = tt* = p - c , we must also have
rl L H L
(14) p = c R + r(c R -c L ).
In light of our analysis of one-period equilibria, it is easy to see
that two types of stationary equilibria exist. First, when y = U = 0» we
have q = L, p = c - cv, , and u~ = c„ - c. . Also, from (6) we find p =
3% - (c -c ), which, when compared with condition (14), shows that the
equilibrium values of a and 3 are
c^+(l+r)(c -c )
(15) a = 3 = — — —.
Obviously, condition (1) is sufficient to guarantee that a = 3 e [0,1].
The second type of stationary equilibrium exists for y = U _> c„/il,. In
this case, as we have seen above, q = H, p = c , and u = uu - c_ • Since
E EL (J H L
q = H, we must have p = (3-u)ir, + c , which together with (14) requires
(l+r)(c -c. )
(16) a = 3 = u + »_Ji_.
Given the range of y, equilibrium a and 3 must satisfy
c^+(l+r)(c -c )
(17) a = 3 > — ^— —.
Again, condition (1) is sufficient for an equilibrium a = 3 e [0,1] to
exist. For any a and 3 that satisfy (17), a corresponding
(l+r)(c H -c L )
Y = \i S [c^/u^, 1 ] can be found from (16) such that all
equilibrium conditions are met. This completes the characterization of the
model's stationary equilibria.
It is clear from condition (17) that the model has a continuum of the
c H +(l+r)(c H -c L )
second-type stationary equilibria parametrized by 3 e [ >1]»
In particular, 6 = 1 is always an equilibrium value, representing the case
where established sellers produce the high quality with certainty and main-
tain their reputations. In this equilibrium, entrants are expected to pro-
(l+r)(c H -c L )
duce the high quality with probability u ■ 1 < 1. However,
unless there are new buyers each period, no entrant actually makes a sale.
This equilibrium obviously Pareto dominates all other equilibria, which have
lower $'s and u's.
Note that in equilibrium, the price charged by established sellers in-
cludes a premium of r(c -c^ ) over the cost of production. This is the mini-
mum premium necessary for inducing sellers to maintain the quality of their
products. Alternatively, the premium can be interpreted as a normal return
on investment in reputation by entrants, t, — C- , which is the cost of
becoming established in one period by charging p = c^ and supplying the
high quality. Thus, the investment takes the form of an introductory bonus
for buyers who are willing to accept an entrant's offer. For a nontrivial
equilibrium to exist, as stated by condition (1), buyers must value the high
quality product more than its cost of production, its moral hazard premium,
and the bonus offered by the entrants.
While these results are quite similar to those of Shapiro (1983), they
are derived from a rational expectations model, whereas Shapiro's argument
is based on adaptive expecations on the part of buyers. The endogenous
entry cost in Shapiro's model is due to buyers' misperception of entrants'
incentives, while in the present model buyers' beliefs about entrants'
behavior are correct and competition lowers the entry price to a level that
reduces the expected profits of entrants down to zero. The difference
between the prices offered by entrants and established sellers is maintained
because the former provide the high quality with a smaller probability. In
equilibrium, both entrants and established sellers are indifferent between
providing the low and the high qualities and choose the high quality with a
probability such that buyers remain indifferent between the two types of
offers. The behavioral assumption that buyers purchase from established
sellers when they are indifferent assures established sellers that they can
keep their customers and continue operation indefinitely as long as they
produce the high quality.
III. Extensions and Generalizations
The simple model developed above demonstrates an endogenous market
mechanism that can potentially resolve the dilemma of markets for high
quality products where moral hazard calls for positive premiums but entry
costs are negligible. The model assumes that entry costs are zero, but it
is easy to show that the presence of positive exogenous entry costs does not
change the essence of our results. Let entry costs be denoted by f. As
long as f ' (c -c )(l+r) the equilibrium price offered by established
sellers will remain at p = c„ + r(c -c_ ) and the entry price will be p_ =
H H L b
c + f. If f > (c -c )(l+r), then p = p = c + rf/(l+r), and the expected
L n L EH
profits from continued operation will be high enough to guarantee the pro-
duction of the high quality with certainty by both entrants and established
Note that the equilibrium in the above model does not depend on whether
the actual quality of each seller's product remains private information for
the buyer who has experienced it or becomes public. Also, if production is
constant returns to scale, the results are unaffected by permitting each
seller to produce more than one unit and to deal with several buyers at the
If production does not exhibit constant returns to scale, it is
necessary to specify in greater detail the process by which sellers become
established and the information buyers receive about the quantity and
quality of each seller's product. However, the principle mechanism
demonstrated by the above model can be put in work in most circumstances:
The offers of established sellers will be determined by a moral hazard con-
dition and the offers of entrants by a zero profit condition, with all
sellers being indifferent between maintaining their reputations and
cheating. In equilibrium, buyers expect established sellers to provide the
high quality with a higher probability and remain indifferent between dif-
ferent offers despite price differences. Then, buyers' decision to continue
with established sellers is sufficient to guarantee that a high quality
equilibrium is maintained.
By "exogenous" entry costs we mean all nonsalvageable costs of setup
and information provision, including signalling costs when adverse selection
among sellers a la Kihlstrom and Riordan (1984) and Milgrom and Roberts
(1986) is a possibility. While many categories of such costs may be endoge-
nously determined in the market, they are exogenous to the moral hazard
problem. All such costs are, of course, barriers to entry, but they may not
be large enough to help the seller moral hazard be overcome.
In fact, under this alternative assumption, the sufficient condition
for the existence of a high quality equilibrium is much weaker than the one
derived in this paper. Instead of condition (1), we would require
U H 2. C H + r ( c H~ c I.) + m ax[0, Cfl-2c[J . The difference between this condition
and (1) is due to the reduction in the introductory bonus by c^ when the low
quality product has to be produced.
Akerlof, G. A., 1970, "The Market for 'Lemons': Quality Uncertainty and the
Market Mechanism," Quarterly Journal of Economics , 84: 488-500.
Allen, F., 1984, "Reputation and Product Quality," Rand Journal of Economics ,
Farrell, J., 1986, "Moral Hazard as an Entry Barrier," Rand Journal of
Economics , 17: 440-449.
Kihlstrora, R. E., and Riordan, M. H., 1984, "Advertising as a Signal,"
Journal of Political Economy , 92: 427-450.
Klein, B., and Leffler, K. B., 1981, "The Role of Market Forces in Assuring
Contractual Performance," Journal of Political Economy , 89: 615-641.
Milgrora, P., and Roberts, J., "Price and Advertising Signals of Product
Quality," Journal of Political Economy , 94: 796-821.
Shapiro, C, 1983, "Premiums for High Quality Products as Returns on Repu-
tation," Quarterly Journal of Economics , 98: 659-680.
3INDERY INC. |
_, u .y\ a J N MANCHESTER.
"** roPk * INDIANA 46962